The equation of the circle, which cuts orthogonally each of the three circles

$$\begin{aligned} & x^2+y^2-2 x+3 y-7=0, \\ & x^2+y^2+5 x-5 y+9=0 \text { and } \\ & x^2+y^2+7 x-9 y+29=0 \end{aligned}$$

Find the equations of the tangents drawn to the circle $$x^2+y^2=50$$ at the points where the line $$x+7=0$$ meets it.

If the chord of contact of tangents from a point on the circle $$x^2+y^2=r_1^2$$ to the circle $$x^2+y^2=r_2^2$$ touches the circle $$x^2+y^2=r_3^2$$, then $$r_1, r_2$$ and $$r_3$$ are in

Find the equation of the circle passing through $$(1,-2)$$ and touching the $$X$$-axis at $$(3,0)$$.